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A Generic Data Model for Describing Flexibility in Power Markets
by
Paul Schott, Johannes Sedlmeir, Nina Strobel1, Thomas Weber2, Gilbert Fridgen, Eberhard Abele3
1 PTW TU Darmstadt
2 PTW TU Darmstadt
3 PTW TU Darmstadt
May 2019
in: Energies (2019), 12(10), p. 1893 The final publication is available at:
https://doi.org/10.3390/en12101893
Article
A Generic Data Model for Describing Flexibility in Power Markets
Paul Schott1,* , Johannes Sedlmeir1 , Nina Strobel2 , Thomas Weber2, Gilbert Fridgen3 and Eberhard Abele2
1 Project Group Business & Information Systems Engineering of the Fraunhofer FIT, 95444 Bayreuth, Germany; johannes.sedlmeir@fit.fraunhofer.de
2 Institute of Production Management, Technology and Machine Tools, Technische Universität Darmstadt, 64287 Darmstadt, Germany; n.strobel@ptw.tu-darmstadt.de (N.S.); t.weber@ptw.tu-darmstadt.de (T.W.);
abele@ptw.tu-darmstadt.de (E.A.)
3 FIM Research Center, University of Bayreuth Project Group Business & Information Systems Engineering of the Fraunhofer FIT, 95444 Bayreuth, Germany; gilbert.fridgen@fim-rc.de
* Correspondence: paul.schott@fit.fraunhofer.de; Tel.: +49-921-55-4734
Received: 20 April 2019; Accepted: 15 May 2019; Published: 18 May 2019 !"#!$%&'(!
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Abstract:In this article, we present a new descriptive model for industrial flexibility with respect to power consumption. The advancing digitization in the energy sector opens up new possibilities for utilizing and automatizing the marketing of flexibility potentials and therefore facilitates a more advanced energy management. This requires a standardized description and modeling of power-related flexibility. The data model in this work has been developed in close collaboration with several partners from different industries in the context of a major German research project.
A suitable set of key figures allows for also describing complex production processes that exhibit interdependencies and storage-like properties. The data model can be applied to other areas as well, e.g., power plants, plug-in electric vehicles, or power-related flexibility of households.
Keywords:demand side management; demand response; generic flexibility data model; flexibility modeling; power system; industrial processes; digitalization
1. Introduction
In the past, only a few large power plants, mainly running on fossil or nuclear fuels, were responsible for the reliable supply of electricity [1]. The continuous expansion of renewable energy sources enables a more sustainable design of the electricity system [2]. At the same time, however, new challenges are emerging [3]. The main challenge is the fluctuating electricity production caused by the weather dependency of wind turbines and photovoltaic plants, which make up a large proportion of renewable energy sources. Moreover, due to the merit order effect, renewable energy sources successively replace conventional power plants [4]. These have so far provided most of the required flexibility [4]. Thus, there is an increasing need for flexibility in the power system to keep ensuring the necessary balance between power generation and consumption. This is called the flexibility gap [5].
In particular, flexibility can address the challenges caused by both foreseeable and unforeseeable fluctuations of renewable energy sources and therefore help to establish an environmentally friendly, decarbonized electricity system [5–7].
Lund [3] and Müller [8] differentiate between four types of flexibility in the electricity system which guarantee security of supply: grid expansion, energy storage, flexibility on the supply side, and flexibility on the demand side. Here, flexibility on the demand side refers to the possibility of deviating from the planned load profile [9]. Typically, such deviations are economically motivated
Energies2019,12, 1893; doi:10.3390/en12101893 www.mdpi.com/journal/energies
by price signals. If a third party sends a signal to a flexible consumer, this is called demand response (DR) [9]. Due to high costs for storage systems and grid expansion, flexibility on the demand side will play an important role as it offers flexibility at comparatively low marginal costs [10–12].
The digital transformation of the electricity sector is opening up new opportunities for utilizing and automatizing the marketing of flexibility potentials [13,14]. For example, the use of smart meters enables improved monitoring and control of electricity consumption and therefore a higher automation level of flexible industrial production systems. Hence, the advancing digitalization on the one hand facilitates an efficient and repeated use of flexibility. On the other hand, it also provides digital communications technology to detect and react to local changes in power consumption in the electricity network, the so-called Smart Grid [15]. With these tools at hand, it is possible to tackle the aforementioned flexibility gap from both the perspective of flexibility providers and from a systemic point of view [12]. Since interoperability in a Smart Grid is an essential requirement, the uniform description and modeling of flexibility is of crucial importance for the optimal scheduling and successful use of flexibility [16,17]. The “Smart Grid Architecture Model” [18] is a framework to support the development of the European Smart Grid. It consists of the following five layers: business layer, functional layer, information layer, communication layer, and component layer. The information layer is meant to provide a data model which ensures a common understanding of the exchanged data.
For an electricity system in which conventional power plants provide the main contribution to flexibility, typically a few key figures, such as activation duration (ramp up time), holding duration (length), and power (capacity) characterize a flexibility [19]. However, as already mentioned, in the future electricity system, one will need new participants who provide flexibility [5]. On the demand side, the industrial sector is of particular relevance as it consumes a large part of the electricity in many countries [20]. Already today, some electricity-intensive companies are optimizing their power purchases, taking their available flexibility potential and price fluctuations into account. However, due to various barriers, such as know-how, or technical, economic, environmental, regulatory, and organizational challenges, many industrial companies have not yet exploited their DR potential [5,8,21]. Standardization can improve the exchange of information and foster access to flexibility-related services. Therefore, it can contribute to a substantial decrease of these barriers, in particular these related to know-how, technical, and economic challenges. In this context, a standardized modelling of flexibility, which can be implemented by a generic data model, takes on an essential part [14]. Such a data model should facilitate the description of any flexibility as precisely as possible on the basis of various key figures.
At the same time, it has to feature an adequate degree of generality in order to capture all kinds of flexibility providers.
Some contributions in literature already deal with the description of power-related flexibility.
For example, Reference [22] designed a taxonomy for modeling flexibility. In order to characterize different types of flexibility, the authors defined the taxonomy “buckets”, “battery”, and “bakery”.
These types exhibit various key figures such as power states, energy capacity, energy level at a specific deadline, and minimum runtime. In [23], the authors developed a clustering of flexibility into four groups: load curtailment, load shifting, onsite generation, and utilizing electricity storage systems.
Each group is described by various constraints. Based on that, the authors derived a decision-making model for DR aggregators in wholesale electricity markets. However, those forms of flexibility have been modeled in a simplified way and a precise description of the flexibility of industrial processes is not possible with this approach. Additionally, the authors use different key figures for each cluster, making the model rather unwieldy. Finally, based on an in-depth literature review, Reference [24]
presents a more generic approach in their work. They define a catalog of features whose generic optimization models must take into account to describe all possible kinds of flexibility (see Section6).
However, our work in a major German research project shows that also this catalog and in particular its implementation exhibit several shortcomings. The following three aspects outline the contribution of our work:
• We propose a generic data model which we developed in the course of a major German research project to model power-related flexibility. The modular structure of the data model allows us to precisely describe different types of flexibility.
• The data model allows transferability among different sectors and hence provides an opportunity for standardization. It therefore constitutes a basis for integrating flexibility into information systems and thus improved information exchange and a higher automation level. This allows for automating the use of flexibility.
• We validate our data model in close collaboration with companies from a major German research project. In the process, it has been demonstrated that the data model is suitable to represent flexibilities with different characteristics of the companies.
The focus of this article is on the description of generic power-related industrial flexibility, although our results are sufficiently generic to also apply to households [25], small-scale industries, trade, services [26], and supply side flexibility. Electric cars will also become increasingly important as novel participants in the electricity system [27,28]. The data model can also be applied to the charging and discharging of electric cars. Usually, flexibility exhibits one or more degrees of freedom and can therefore be regarded as a subset of a multi-dimensional space. In order to describe a specific instance of a flexibility, i.e., an element of this space, we also present a data model for what we will call flexibility measures.
The remainder of this paper is organized as follows. In Section2, we describe the research project in which we developed and validated our generic data model. Next, in Section3, we present the proposed data model for industrial flexibility by discussing the involved subcategories. In particular, we explain the need for and limitations of each of the subcategories’ key figures. In Section4, we then derive the corresponding data model for flexibility measures. Afterwards, we present how the data model can be used for different applications by means of two exemplary use cases in Section 5.
In Section6, a discussion compares our data model with existing work. Finally, Section7summarizes the main findings and gives an outlook on future research.
2. Empirical Foundations
As already mentioned, the data model was developed in a major German research project, namely “SynErgie”. It is part of the program “Kopernikus projects for the Energiewende” which develops technological and economic solutions for the transformation of the energy system. It consists of an interdisciplinary consortium which involves more than 80 partners from science, industry, and civil society. The SynErgie project aims to synchronize the energy demand of industrial production processes with the fluctuating power supply from renewable sources. For this purpose, a highly dynamic meta-platform based on modern information and communication technology is developed in order to connect companies with flexibility markets and supporting services [14]. Consequently, this platform requires a standardized description of companies’ flexibilities. In the course of the project, we were able to develop and discuss the data model in close collaboration with our scientific partners as well as companies from the following electricity-intensive sectors: steel and aluminum production, chemical industry, machinery and plant engineering, and paper, food, cement, and car industries.
In Germany, these sectors account for approximately 90% of the net industrial electricity demand and 40% of the whole net electricity demand. We conducted several workshops and project meetings with experts from the involved companies. Moreover, we modeled different flexibilities of various project partners and validated them in tests. In particular, the description of these real-world flexibilities guided us through our research and helped to develop and successively improve the data model which we present in the following.
3. Proposed Generic Flexibility Data Model
3.1. Heuristics
Modeling is generally a systematic abstraction of the real world. On the one hand, one has to describe the real world with sufficient accuracy. On the other hand, the model must be as simple as possible, in particular in case it is meant for practical applications. It is therefore necessary to make simplifying assumptions in the right places. After giving an overview of the subcategories of our data model (this Section), we will derive the corresponding key figures, explain why they are necessary, and discuss the underlying assumptions and simplifications in Sections3.2–3.4.
Our data model for flexibility contains components which can be chosen from three subcategories:
flexible loads, dependencies, and storages. We define aflexibilityas a collection of such components.
A flexibility has to contain at least one flexible load. It may, however, exhibit any number of dependencies and storages. Figure 1schematically visualizes the basic idea of the modular data model based on two exemplary flexibilities. Flexibility 1 exhibits three flexible loads. Moreover, flexible load 1a and 1b are interrelated by a dependency. The reader might consider the following illustrative example for such a constellation: a graphitizing oven exhibits two production phases which are represented by flexible load 1a and flexible load 1b. The second phase (flexible load 1b) always follows the first phase (flexible load 1a). The dependency then can describe that flexible load 1b requires the usage of flexible load 1a some time in advance. Flexible load 1c is an independent production machine, which at the same time exhibits flexibility. Flexibility 2, which can be associated with the same or another company, features two flexible loads, one dependency, and two storages.
One storage is linked to two flexible loads, whereas the second storage is linked to only one flexible load. For instance, flexible load 2a and 2b can be two machines that manufacture the same product in different ways and store it in the product warehouse (storage 2a). Dependency 2 then accounts for the fact that the machines must not be operated simultaneously. Moreover, flexible load 2b utilizes the generated waste heat and stores it in a heat reservoir (storage 2b). As Figure1illustrates, dependencies and storages always refer to flexible loads among the flexibility. In other words, a flexibility is a closedobject.
Flexibility 2 Flexibility 1
dependency 1
flexible load 1a
flexible load 1b
storage 2a
dependency 2
flexible load 2a
flexible load 2b storage 2b
flexible load 1c
Figure 1.The generic data model enables a uniform and modular description of industrial flexibility.
We regard a power-related flexibility as the opportunity to deviate from the original schedule with a resulting change in power consumption. Typically, a flexibility originates from one or more devices (units, machines). Such devices can exhibit different degrees of freedom regarding how they
may operate, e.g., at different times or energy levels. We call the flexibility associated with an isolated device aflexible load. Our modelling of a flexible load will be detailed in Section3.2. One can take into account the aforementioned degrees of freedom by representing each dimension by an associated key figure. A flexible load therefore parameterizes a set of individual load curves which can be realized by the flexible device. We call a single usage of a specific realization aflexible load measure. It can be imagined as a specific choice from the range of each key figure of a flexible load. The corresponding key figures which describe the flexible load measure will be denoted initalicswith an attached asterisk (⇤).
We will explain flexibility measures and flexible load measures in detail in Section4. Thus, a filled data model for a flexible load does in general not only contain numbers, but also subsets (ranges) of a corresponding basic setS. In other words, they are elements of the corresponding power sets 2S =P(S). Moreover, the key figures of a flexible load may have intrinsic interrelations. This means that not every key figure can be chosen freely from its associated base set. In other words, the choice of one key figure might restrict the accessible values for another key figure. For instance, some choices of key figures might be functions of the choices of other key figures within a flexible load measure and thus implicitly defined. Of course, we could in principle also define a separate flexible load for any combination of interrelated key figures. However, with the possibility of dependent key figures, the flexibilities can be defined more compactly and the partition of the process into flexible loads is more intuitive. In Section5, when we will have given a detailed explanation of the key figures, we will give illustrative examples for this property. Imagine that (ignoring units) the value ofkey figure 1may be chosen freely in the intervalS= [0, 10]andkey figure 2(also ignoring units) always has to be twice the value ofkey figure 1. Then, one would be tempted to write the following:
key figure 1= [0, 10];
key figure 2=2⇥(key figure 1).
Sincekey figure 1is given by a set, one would interpret the function f :x7!2xas a set-valued function, the result being the image set of[0, 10]under f and hencekey figure 2= [0, 20]. This would give the impression that the value ofkey figure 2, i.e.,key figure 2⇤, may be chosen freely within the interval[0, 20], which is clearly not what we intended. What we wanted to say is that for every flexible load measure specified by the corresponding flexible load, the functional relationship between the associated key figures must hold:key figure 2⇤=2·(key figure 1⇤).
If there are several flexible loads involved in an industrial process, one might expect that one can represent this in our data model by simply moving to product spaces, i.e., arbitrary combinations, of flexible loads. However, we observed that, in reality, we cannot assume that a flexible load is always isolated. Consequently, similar to what we explained for intrinsic interrelations of key figures within a flexible load, also key figures from different flexible loads might be related. Thus, not all of the aforementioned product space is accessible. From our observations in SynErgie, we learned that it is usually sufficient to consider only logical interrelations among pairs of flexible loads. They are typically related to certain requirements on process sequences. We will call the subcategory which describes such interrelationsdependencies. A dependency thus connects key figures from the two involved flexible loads. This is achieved by defining suitable key figures for dependencies, which in turn refer to key figures of (measures of the) interdependent flexible loads. These will be described in detail in Section3.3.
Finally, we observed interrelations which can be clustered under the common termstorages.
We will introduce storages in Section3.4. It is important to keep in mind that batteries are rather an exception in industrial processes. When thinking about storages, one should rather consider stocks for products in batch processes or reservoirs for heat, cold, or chemical products. Unlike dependencies, storages only pose constraints on the energy consumption of the flexible loads which they are connected to. In other words, the energy content of storage must satisfy certain bounds for all times. Moreover, in contrast to dependencies, storages can also cause costs.
As opposed to flexible loads, both dependencies and storages do not add any degrees of freedom to the flexibility. They pose boundary conditions which restrict the admissible combinations of flexible load measures among which we may choose or optimize in a subsequent step. This explains why we did not allow to define a flexibility which does not contain a flexible load: in this case, the flexibility space would be empty and could thus be ignored. Figure2illustrates two flexible loads each of which are assumed to exhibit one degree of freedom. The respective degrees of freedom are depicted on the two axes. The flexible loads are further interconnected by a dependency as well as storage. Recall the above example where two machines (flexible loads) are connected by a dependency and supply storage. The degree of freedom results fromkey figure 1for both flexible load 1 and flexible load 2.
Figure2illustrates that flexible load 2 has more freedom than flexible load 1. The resulting black area in the middle is the remaining, accessible flexibility: Only certain combinations of measures of the two associated flexible loads are accessible. If there were no constraints involved, any combination of measures from flexible load 1 and 2, i.e., the whole rectangle, would be accessible. An optimization (with respect to a certain objective function) will then choose the “best” element among the (accessible) flexibility, i.e., a flexibility measure, which can then be executed.
The subset of the resulting product space which is not accessible because of a dependency between flexible load 1 and flexible load 2.
The subset of the resulting product space which is not accessible due to a storage for which both flexible loads are suppliers.
The remaining accessible combina- tions of the two flexible loads and hence the flexibility.
The individual flexibilities induced by flexible load 1 and flexible load 2.
Their product space is the flexibility of the system of the two flexible loads without further constraints.
x An element in the flexibility, i. e., a flexibility measure.
flexible load2
flexible load 1
x
The (collections of) flexible load measures which are associated with the individual usage(s) of the respective flexible loads and constitute the flexibility measure.
Figure 2. Our definition of a flexibility, visualized in a setting with two flexible loads with each exhibiting one degree of freedom.
In the following subsections of Section3, we define the key figures of the three subcategories flexible loads, dependencies, and storages.
3.2. Flexible Loads
Let us consider a non-empty planning horizonH⇢R. One would imagine a planning horizon as a certain time interval, e.g., from 8:00 a.m. to 6:00 p.m. on a specific day. It is in general given by a subset of the reals. We decide that the unit is seconds, measured with respect to the common reference point 1 January 1970, which is—apart from units—close to what one would regard a date–time from a programming-oriented perspective. As already discussed, a flexible load describes the opportunity of an isolated device to deviate from the scheduled power consumption. Hence, it can bee seen as a family of mapsp:H!Rwhich associate with every timetin the planning horizonHthe corresponding change in power consumption p(t). Mathematically, we could consider any subset of Abb(H;R), which denotes the set of all functions fromHtoR.
However, in SynErgie, we learned that, for practical purposes, this generality goes too far. In the following, the required key figures for a flexible load are derived from the findings in the project.
It turned out quickly that it is not necessary to include arbitrarily complicated families of load curves p(t)into our model. Rather, for applications, it is sufficient and more practical to restrict to families of mapsp:H!Rwhich can be described by means of periods of constant increase or decrease in load (“modulation periods”), and periods of constant load (“holding periods”). Note that although mathematically periods of constant load are a special case of the former with the rate of change (slope) being zero, we distinguish these periods in order to foster intuition and to account for the different characteristics of the physical processes. One can regard our approximation as a specific linearization of load curves. However, it is important to highlight that we do not linearize a fixed function, but rather a collection of functions, and thus preserve the degrees of freedom. Figure3illustrates an exemplary flexible load measure, i.e., one special load curve in the family which is meant to be parametrized by the key figures of the corresponding flexible load. In Figure3, the different phases and their respective durations are depicted.
power state 1
power state 2
power state 3
end time holding
period 1
activation period
deactivation period
time power
deactivation duration holding
duration 1 activation
duration 1
2
7 holding
period 2 4
holding period 3
6
holding duration 2
holding duration 3
start time total time
modulation period 1
3
modulation period 2
5
modulation duration 1
modulation duration 2
Figure 3.An exemplary flexible load measure with the corresponding parameters.
Apart from power consumption depending on time, a flexible load also exhibits some other relevant characteristics, such as integration in an IT-system or costs, which have to be included in our data model. With this preliminary work, we are now prepared to discuss all the key figures of the subcategory flexible load.
3.2.1. Flexible Load ID
A company can have a large number of devices which exhibit flexibility. Within a company, production is usually managed and controlled via an IT system, for example an ERP system. To be able to easily manage them, a flexible load thus requires aflexible load ID. The available systems must also consider theflexible load IDs. The key figureflexible load IDis used to uniquely identify a flexible load and hence to address the corresponding device in case it is used. As will become clear in Section3.3.1, it is explicitly possible that multiple flexible loads with multipleflexible load IDsrefer to the same device. This key figure is important when execution of a (specific) flexibility measure must be ordered by the IT system of a company.
3.2.2. Reaction Duration
In case the execution of a flexible load measure is ordered, it is highly relevant how long it takes from giving the command to activate until a change in power really starts. For this reason, it is necessary to add the key figurereaction durationto our model. In an automated system, this is comparable to the latency time that occurs during the transmission of signals. For processes that still require a lot of manual effort, thereaction durationcan also refer to other kinds of delay. For example, an employee might need some time in advance in order to prepare a machine accordingly. Therefore, the reaction time can be interpreted as the duration between pulling the trigger and the start time of the flexible load measure. Thereaction durationis of high relevance especially in time-critical applications.
For example, in the case of control power, flexibility must be provided within a short period of time.
Of course, we make the assumption that a company can determine thereaction duration. This is particularly challenging when the response time is not just given by the latency time of an IT system.
Thereaction durationin our data model has the unit seconds and is given by a real number which by causality is non-negative.
3.2.3. Validity
Flexible loads are usually only available within certain time windows. The reason is that, for companies, compliance with delivery obligations naturally has a higher priority than the utilization of flexibility. Hence, restrictions associated with time of use can depend, for example, on the production plan, since this determines when machines operate and could be switched off. Another reason is that machines may have to be maintained and operated during shift times and are therefore not always available. Moreover, for many electricity-intensive companies, technical restrictions or grid fees pose a central boundary condition regarding time periods of increased electricity consumption. Therefore, the key figurevalidityis an essential part of the data model and serves to consider restrictions with respect to availability over time. We use it to define when flexibilities may be used. Consequently, validityis a subset of the planning horizon. As opposed to other key figures, we assume that the validityis fixed and does not depend on any other key figure. As for the planning horizon, our unit here is seconds since 1 January 1970. Recalling the example of shift times, we cannot expect that it is usually an interval. In SynErgie, we have investigated a wide range of flexibilities, some of which have quite special temporal characteristics. For example, it is common for some companies to start flexible processes within a certain time window. By contrast, other processes have to be completed at a certain point in time. Another observation was the necessity to define a time window in which the whole execution of a flexible load must be completed. Therefore, we need to define thevaliditywith respect to a certain reference. Based on our observations, the following three references are necessary:
“start”, “total”, and “end”. The reference “start” indicates that the start time of a flexible load measure must lie within thevalidity. Similarly, the end of a flexible load measure must lie within the defined interval for the reference “end”. The reference “total” specifies that the entire load profile of a flexible load measure must lie in the interval specified by the key figurevalidity. This distinction is particularly relevant for flexible loads with many degrees of freedom. For these, start time, end time, and total time can usually not be converted into each other at the level of a flexible load. As already mentioned, these three references were sufficient in order to encompass all the flexible loads which we encountered in SynErgie. However, one could think of special cases which can not be expressed by any of the three proposed references. For example, imagine that the first half of a process must be completed within thevaliditysince it must be supervised by an employee. However, note that, by splitting this example into two separate flexible loads and defining suitable dependencies (see Section3.3), one could even model such cases with our data model.
3.2.4. Power States
As already discussed, industry processes can usually operate at different levels with regard to power consumption. That is why we introduce the key figurepower states. It defines the admissible power levels of the plateaus, i.e., during holding periods (see Figure3. Depending on the choice of perspective, both the absolute power values and the deviation from the scheduled load can be defined aspower states. Withpower states, we describe situations in which devices have a constant power consumption. Of course, these can also be very short periods of time. Power statesfor subsequent holding periods may be different, in fact, this is the case for all variables which need to be specified repeatedly. For the key figurepower states, both continuous and discrete subsets of the real numbers are possible as basic sets. Continuouspower statesoccur, for example, in cooling units. Here, the power consumption can be set almost arbitrarily within a specific interval. On the other hand, there are processes, e.g., electrolysis, in which only discretepower statesare permitted. The unit forpower statesare chosen to be kW. A positive resp. negative sign represents an increase resp. a decrease in electricity consumption.
In reality, the actual electricity consumption is rarely constant. However, in the energy industry, the time interval of 15 min is established as the shortest observation period. On power markets, for example, the products with the shortest duration are 15-min products. This implies that our assumption of constant consumption in certain segments is practicably as good as an exact modelling.
In this case, it is important to keep in mind that the key figurepower statedoes not precisely represent the actual physical state.
3.2.5. Holding Durations
As we already mentioned above, the key figurepower statesis related to temporarily constant states. Machines often need electricity for a certain period of time, e.g., to manufacture a product.
The durations ofpower statesare specified by the key figureholding durations. Theholding duration specifies the range in which the chosenpower statemay be held. As a unit, we choose the SI base unit seconds. Analogous to thepower states, we adopt the simplified view that the actual duration is known exactly in advance. Of course, in reality, it can happen that processes are completed earlier or later than planned.
3.2.6. Usage Number
In practice, we observed many flexible loads which admit multiple runs within theirvalidity.
For instance, when manufacturing a product, a production step must be repeated. To avoid the need for defining several identical flexible loads which are mutually exclusive during their time of use, the data model contains the key figureusage number. It describes the number of permitted activations (usages) of a flexible load within itsvalidity. Theusage numberis given by a subset of the natural numbers (including zero). We want to emphasize that it is not necessary to select identical flexible load measures in repeated usages. For example, ifpower state⇤1 was selected for the first usage, a different power state2⇤can be selected for the second use. However, by definition, the corresponding ranges can depend on the usage number⇤. For instance, in a thermal process, it is likely that multiple usages will require either a smallerpower stateor a shorterholding duration. If a company is aware of these relations, thepower statesin this example could be a function of theusage number.
3.2.7. Modulation Number
So far, we have had the picture in mind that flexibilities have exactly one holding period, after which the load profile returns to the zero state. However, there are many processes that can adapt theirpower stateduring one usage several times (see Figure3). A usage refers to the sequence of:Power stateis equal to zero, followed by some changes in power consumption, and ends again with apower stateof zero. As an example, one can think of heating processes, which modulate theirpower states
from time to time. In addition to industrial processes, power plants can also be considered: As soon as these are operated, thepower statechanges several times before the power plant is switched off again.
This leads to the key figuremodulation number. It states the number of modulations (changes of the power state) which may take place during one usage of the process. Activation and deactivation are regarded as special cases of a modulation, since the restrictions posed on the initial and final power change are often different from the ones posed on modulations in between. Themodulation numberis given by a subset of the natural numbers.
3.2.8. Activation Gradient, Modulation Gradients, and Deactivation Gradient
With regard to the activation, modulation, and deactivation phases, the intensity or speed of the power change is a relevant parameter. It can, for example, be restricted due to constraints when heating material. Moreover, many devices cannot be switched off at arbitrary speed. We introduce the key figuresactivation gradient,modulation gradients, anddeactivation gradient. The corresponding durations can easily be calculated from the respective gradient and the difference in neighbouring power statesto be reached. Respecting the units forpower statesandholding durations, we define the unit to be kWs . All gradients are given by subsets of the extended real numbers, i.e., we also allow plus and minus infinity as legitimate gradients. This makes sense with the convention ±1• := 0, since in an optimization the only relevant quantities are energy consumption and time which are both indirectly proportional to the gradients. Theactivation gradientresp. deactivation gradientspecifies which slopes the load curve can exhibit during the activation resp. deactivation phase. The key figure modulation gradientsis the analog for modulation phases. Theactivationanddeactivation gradientsare required in addition to themodulation gradientsince the speed of activation and deactivation often differ from a modulation. If a machine has already been warmed up, it can usually change its output more quickly. Thus, it is likely that themodulation gradientsmay depend on previouspower statesand theholding durations. Thedeactivation gradientis the analog of theactivation gradientfor the deactivation phase. We adopt the convention that a positive gradient for activation, modulation, and deactivation always means that power consumption increases with time. As forpower statesandholding durations, we simplify the real world by linearization here.
3.2.9. Regeneration Duration
Often, one has to wait some time after a flexible load measure has been activated until another flexible load measure from the same flexible load may be activated again. This might be necessary for maintenance, chilling, or warming of the corresponding machine or product before reuse. In processes that are not yet highly automated, employees often need to remove the finished product from a machine and load the raw materials into the machine again. This characteristic must be taken into account especially for flexible loads with potentially multiple usages. Therefore, we include the key figureregeneration durationinto the flexible load data model which specifies the time span in which, after completion of a flexible load measure, the flexible load must not be activated again. In other words, theregeneration durationrefers to the minimum waiting time in seconds after the end of a flexible load measure. Aregeneration durationof 0 seconds means that right after a flexible load measure has ended, another flexible load measure from the same flexible load may be activated. In practice, this key figure often depends on the characteristics of other key figures. If, for example, theregeneration durationis caused by a cooling process, theregeneration durationcan probably depend on the previously attainedpower statesandholding durations. This also goes along with the limitation that these relations must be exactly known in advance in order to be able to model theregeneration durationexactly.
3.2.10. Costs
The flexible operation of machines usually causes additional costs. They might stem from higher expenses, e.g., due to higher wear and tear of machines in atypical operation. It is also conceivable that increased personnel hours and associated expenses such as handling and maintenance must be accounted
for here. In addition, for some machines, manufacturers give a warranty covering a certain number of power changes. As soon as this is exceeded due to frequent usage of a flexible load, the warranty for the corresponding machine expires. This circumstance must also be taken into account.
For this reason, the key figurecostsis also part of the data model. The unit of this key figure is the chosen currency, in our case, Euro. We explicitly do not include electricity costs in this key figure.
The reason is that these depend on company-extrinsic parameters such as (expected) electricity price and are not necessarily known in advance. However, from integrating the productp(t)·p(t)where p(t)denotes the (expected) electricity price at timet 2 H, one can easily calculate the (expected) electricity costs. The key figurecostsis likely to have dependencies on other key figures. For example, high values forpower statesor gradients can influence the degradation of the infrastructure and thus the associated costs. With regard tocosts, the limitation is that companies must know the relations exactly.
Otherwise, if the exactcostsare unknown, one can define a threshold value to consider an increased risk of wear and tear. In the end, thecostsdecide whether a flexibility is used or not. Therefore, they must be modelled as accurately as possible. However, since most industrial machines are designed for continuous operation, thecostsincurred are often not known.
3.2.11. Summary: Flexible Loads
Table1provides an overview of all presented key figures which we use to describe flexible loads.
With regard to the convention of plural or singular key figures, we have defined the following: key figures that can have more than one value during one usage are denoted in the plural, the remaining key figures—apart from costs—are in the singular.
Table 1.Key figures for flexible loads.
Key Figure Type Unit Description
Flexible load ID String - An identifier for the flexible load that might be used by an IT system in order to manage it. Theflexible load IDserves for fast and easy identification, especially if there is a large number of flexible loads present.
Reaction duration 2R+0 s The time between pulling the trigger and the start of a flexible load measure.
This key figure is of interest for correct and timely execution of usage commands.
Validity 2H⇥{”start”,
“total”, “end”} s
The subset of the planning horizon at which the flexible load is available.
The three references (“start”, “total”, and “end”) define which parts of the total time of associated flexible load measures must lie in thevalidity.
Power states 2R kW
The powers at which the flexible load can run during each of the (modulation number+1) holding periods. A positive sign means that the flexible load causes an increase of electricity consumption, negativepower statesrepresent a decrease in consumption.
Holding durations 2R s The lengths of time periods for which the flexible load runs at itspower states.
Every holding period is the time with constantpower statebetween two consecutive modulations, including activation and deactivation.
Usage number 2N - The permitted number of usages of the flexible load in the planning horizon.
Modulation number 2N - The number of allowedpower statemodifications within one usage of a flexible load, excluding the two modulations which correspond to initial activation and final deactivation.
Activation gradient 2R[{±•} kW·s 1 The rates at which the power curve can change its power at initial activation.
If thepower stateincreases, theactivation gradienthas a positive sign.
Modulation gradients 2R[{±•} kW·s 1 Analogous to theactivation gradientfor the modulation periods.
Deactivation gradient 2R[{±•} kW·s 1 Analogous to theactivation gradientfor the final deactivation period.
Regeneration duration 2R+0 s The time for which, after the deactivation of a measure from the flexible load is finished, no (other) measure from the same flexible load must be activated.
Costs 2R e Thecostsassociated with the use of the flexible load, electricity costs excluded.
3.3. Dependencies
As already mentioned in Section3.1, we observed that there are often logical constraints among different flexible loads. A dependency describes the impact of an activation of a measure corresponding to a certain flexible load on another measure from a different flexible load. We observed that two logical types, namely implication and exclusion among pairs of flexible loads, are sufficient in order to describe those logical constraints. However, extension to more flexible loads as inputs would be straightforward, but would also make the data model more complicated. In the following, we describe the key figures which specify a dependency.
3.3.1. Trigger Flexible Load, Target Flexible Load, and Logical Type
A dependency always refers to a pair of flexible loads. Therefore, we introduce the two key figurestrigger flexible loadandtarget flexible load. This means that usage of any of the flexible load measures from thetrigger flexible loadposes some constraint on the usage of thetarget flexible load.
In addition, it is necessary to describe the dependency type. By an “implies”-dependency, we mean that, for every usage of a flexible load measure from thetrigger flexible load, some uniquely associated flexible load measure from thetarget flexible loadmust be activated. In particular, the usage number⇤of thetrigger flexible loadin the planning horizon cannot be larger than the usage number⇤of thetarget flexible load. We realized the need for the “implies”-dependency for the following situations:
In several production processes, a certain order of steps needs to be fulfilled. As another example, if the output is reduced at a certain point in time, the production that has to be renounced must be recovered at a later stage by increasing the output.
On the other hand, an “excludes”-dependency states that the usage of some flexible load measure from thetrigger flexible loadforbids usage of any of the flexible load measures in thetarget flexible load.
The “excludes”-dependency is necessary, for example, in order to avoid consumption peaks, which are relevant for network charges. Moreover, it can be used to model a device which is involved in very different processes such that the flexibility associated with this device can not be described by only using a single flexible load.
Note that, by combining two dependencies with suitable trigger flexible loads, target flexible loads, andlogical types, one can also model further logical interrelations such as “if and only if” and
“exclusive or”.
3.3.2. Temporal Type and Applicability Duration
In order to respect the temporal characteristics of the dependencies that we observed in SynErgie, we also introduce the key figures:Temporal typeandapplicability duration. The reason is that, for both
“implies”- and “excludes”-dependencies, one must be able to specify the period for which these dependencies are valid. The key figure applicability durationrepresents this property. It is given by a subset of the real numbers (typically an interval) and has the unit seconds. In the case of an
“implies”-dependency, theapplicability durationstates that within the specified period thetarget flexible loadmust be activated. Similarly, for an “excludes”-dependency, theapplicability durationindicates that thetarget flexible loadmust not be used during this time.
Theapplicability durationcan have different reference points. Thus, analogous to our approach for the key figurevalidity, we need to add a time reference. Therefore, we introduce the key figure temporal type. Since the reference must be applied to both thetrigger flexible loadand thetarget flexible load, thetemporal typeis given by a tuple, consisting of combinations of “start”, “total”, or “end” in both components. The first component refers to the temporal reference for thetrigger flexible load, the second to thetarget flexible load. Combiningapplicability durationandtemporal type, a flexible load measure from thetrigger flexible loadyields an interval in which the flexible load measure of thetarget flexible loadmust or must not lie.
Figure4visualizes some possible combinations of these two key figures. For a specifiedtrigger flexible load A, the figure illustrates the accessible times for the usage of thetarget flexible load B.
The holding duration of flexible load A is fixed and given as depicted, and theapplicability duration is given by[ 30 s, 60 s]. The orange bars denote the part of the planning horizon in which—once a measure in flexible load A has been determined and hence in particular the temporal component is specified—a measure from flexible load B may be activated. For simplification, we assume that the temporal component for flexible load B is also fixed. Then, the part of the total usage duration of flexible load B which is coloured in orange must lie within the orange bar.
(fixed) start of flexible load A (fixed) end of flexible load A
“implies“× (“ total“, “total“)
0 60 90 150
-30
“implies“× (“start“, “start“)
“excludes“× (“end“, “end“)
“excludes“× (“total“, “total“)
(possible) start of flexible load B. In this example, the start of flexible load B
must lie within the orange range.
(possible) end of flexible load B
time in s
The range where the orange part (characterized by“start“, “total“, or“end“) of the total time of flexible load B must be located.
An exemplary use of flexible load B.
holding period of flexible load A
lower bound of applicability duration (-30 minutes) from the start of flexible load A
upper bound of applicability duration (60 minutes) from the start of flexible load A
Figure 4.Logical type, temporal type, and applicability duration.
The following practical examples further illustrate the possibilities of combining dependencies with differentapplicability durationandtemporal type. Thetrigger flexible loadis called “C” and the target flexible loadis called “D”. Firstly, due to process interdependencies, C and D should not be active at the same time. For this example, logical typehas the value “excludes”, theapplicability duration is[0, 0] and thetemporal typeis{“total”, “total”}. Secondly, as the material has to be replaced in machines after completion of process C, further processing D can be carried out at the earliest 20 s after completion of C. At the same time, D must be completed two minutes after C at the latest.
Therefore, two additional dependencies must be defined: One withlogical type“excludes”,applicability duration[0, 20], andtemporal type{“end”, “start”}ensures that D does not start earlier than 20 s after C.
The second dependency withlogical type“implies”, applicability duration[0, 120], andtemporal type {“end”, “end”}ensures that D ends two minutes after C at the latest.
Finally, we want to highlight that—strictly speaking—theregeneration durationwhich we defined for flexible loads is a special case of a dependency. In this case, triggerandtarget flexible loadare identical, andlogical type,temporal type, andapplicability durationare given by: “excludes”, (“end”,
“start”), [0,regeneration duration⇤]. However, theregeneration durationcan be regarded as an intrinsic property of a flexible load, and only requires the specification of one parameter, which led us to define it as a separate key figure.
3.3.3. Applicability Conditions
In the case of dependencies between two flexible load measures, in SynErgie we have often observed that there are additional conditions which need to be fulfilled. These can be defined in
the key figureapplicability conditions. Every condition is described by an equation which refers to key figures of the two involved flexible loads. The first resp. second component of the tuple which represents the equation are regarded as left resp. right-hand side of the equation. Theapplicability conditionsare regarded to be satisfied if for everyi2{1, . . . ,n}, both components of theith component ofapplicability conditionshave the same value. A constraint posed by a dependency which exhibits applicability conditionsare not satisfied, the dependency is regarded is only then regarded as fulfilled if theapplicability conditionsare met. In other words, an activation of thetrigger flexible loadimplies an associated activation of thetarget flexible load—respecting the constraints given by the other key figures—in a configuration (measure) such that theapplicability conditionsare satisfied.
As an illustrative example, imagine a process in which flexible load A describes the opportunity to reduce power consumption at a given point in time. By means of flexible load B, the energy can then be recovered. For instance, due to losses in efficiency, flexible load B must make up 1.5 times the energy of flexible load A. Therefore, theapplicability conditionis given by the tuple(energyB, 1.5⇥energyA). The pre-factor of 1.5 means that flexible load B must consume 50% more power due to losses, which enforces the following equation:
energyB= 1.5⇥energyA. (1)
Flexible load A has only onepower state{ 500 kW}, but a variableholding durationwith permitted range[600 s, 3000 s]. Themodulation numberis zero in this case. Flexible load B, on the other hand, has the fixedholding duration{900 s} and a variablepower state([0 kW, 10,000 kW]). The constraint in Equation (1) specifies that thepower stateof flexible load B must be chosen according to the configuration of flexible load A. The relevantpower statecan be calculated as follows. First, it is necessary to calculate the electricity consumption of flexible load A. For a givenpower state, the power consumption of flexible load A which corresponds to the area of the rectangle (the gradients are assumed to be infinite here) is as follows:
energyA=power state⇤A⇥holding duration⇤A
= 500 kW⇥holding durationA⇤. (2)
The power consumption of flexible load B is calculated as follows, whereby theholding duration is given:
energyB=power state⇤B⇥holding duration⇤B
=power state⇤B⇥900 s. (3)
By merging Equations (2) and (3), the additional constraint—which ensures that flexible load 2 catches up 1.5 more electricity than flexible load 1—can now be determined:
power stateB⇤⇥900 s=1.5⇥500 kW⇥holding duration⇤A, (4)
power state⇤B= 1.5⇥500 kW⇥holding duration⇤A
900 s . (5)
This example illustrates which additional restrictions can be modelled by the key figure applicability conditions.
3.3.4. Summary: Dependencies
Table 2 summarizes all key figures of the dependency subcategory including type, unit, and description.
Table 2.Key figures for dependencies.
Key Figure Type Unit Description
Trigger flexible load String - The ID of the flexible load which triggers the dependency.
Target flexible load String - The ID of the flexible load which is affected by thetrigger flexible load.
Logical type {”implies”,
”excludes”} -
Specifies whether a usage of thetrigger flexible loadrequires that thetarget flexible loadis also used (“implies”) or prevents that thetarget flexible loadmay be used (“excludes”).
Temporal type {”’start”, “total”,
“end”}2 -
The parts (“start”, “total”, “end”) of thetrigger flexible load (first component) and thetarget flexible load(second component) which are affected by the dependency.
Applicability
duration 2R s
The time period for which, after usage of thetrigger flexible load, thetarget flexible loadmust be activated at least once (“implies”) resp. not at all (“excludes”). Hereby, one has to keep in mind the relevanttemporal type.
Applicability conditions
⇣2R⇥2R⌘n -
Additional conditions which have to be satisfied such that the dependency is regarded to be fulfilled. In other words, an activation of thetrigger flexible loadimplies an associated activation of thetarget flexible loadin a configuration (measure) such that theapplicability conditionsare satisfied.
3.4. Storages
Energy storages are classically understood to be electrical storage devices such as batteries that have a certain storage capacity. Apart from these conventional storage systems, industrial processes often have storage potentials that can be described with similar key figures. They usually appear in form of stock for batch processes, thermal inertias, or reserves of intermediate products such as chemicals. The form of energy in a storage device is not limited to electrical energy. All forms of effective energy, e.g., heat, cold, and compressed air, whose provision is connected to a flexible load and any product whose manufacturing (or disposal) requires electrical energy can theoretically be stored. In the following, we present the key figures which are necessary for describing storage.
3.4.1. Storage ID
Just as it is important for flexible loads to have a clear designation (see Section3.2.1), it is also for storage systems in industrial processes. Therefore, the key figurestorage idis implemented. This key figure is an identifier for storage in the company’s IT system and assigns a unique name to the respective storage system. This is particularly important if a storage is connected to several flexible loads or if one flexible load can supply different storages (see Figure1). For example, an intermediate product or raw material warehouse can serve different devices.
3.4.2. Usable Capacity
The indication of capacity is indispensable for the characterization of a storage facility as it limits the quantity of the good resp. energy to be stored. Therefore, the key figureusable capacityis part of the data model. However, in the context of energy flexibilization, it is often not the maximum energy content of a storage facility that is relevant, but the proportion available for flexibilization.
One example are thermal storages. While, from a physical point of view, one would have to refer to the ambient temperature or the temperature zero point when calculating the energy content, the capacity of interest in the context of energy flexibility is usually limited by the minimum and maximum process temperatures allowed. Batteries are another example. With a nominal storage capacity of 30 kWh,
theusable capacity(which in literature is sometimes also-called useful capacity in the context of batteries) might be restricted, for example to extend the lifetime of the battery storage, as this is depending on the depth of charge and discharge cycles [29]. Although not all storage systems directly refer to energy quantities, a representation in the form of energy quantities is reasonable in order to compare different types of storages and suppliers (see Section3.4.6). For example, the energy content of a thermal storage can be compared with that of a compressed air system. Theusable capacityis specified as an interval in kWh whose lower bound may never be undershot and whose upper bound may never be exceeded by the energy content of the storage.
3.4.3. Initial Energy Content
It is important to specify the energy content in the storage—theinitial energy content—at a specific time stamp. For example, a fully charged storage facility cannot be used directly to provide a load increase. If the storage facility is operated over several charging cycles during long planning periods, the initial energy contentusually has less influence on the result than if only one charging cycle is considered. This key figure is specified in kWh and the corresponding time stamp in seconds.
3.4.4. Target Energy Content
In some cases, a specific energy level must be reached in the storage at a certain point in time.
Examples for this are batteries of intralogistics vehicles, which should be fully charged at the beginning of a shift. Another example are product warehouses, which must be full as soon as the delivery date is due. These circumstances can be defined in the key figuretarget energy contentwith a corresponding time stamp. It is not necessary and expedient to specify an exacttarget energy contentin all cases.
Often it is sufficient to know which upper and lower limits must not be exceeded for the energy content of the storage (usable capacity). In general, thetarget energy contentis defined as a subset of the usable capacity. Its unit is kWh and the time stamp is given in seconds.
3.4.5. Energy Loss
Many storage types are characterized by time-dependent losses of the medium to be stored.
For example, the temperature of thermal storage tanks adjusts to the ambient temperature over time, which means that the exergy to be stored gets lost. Compressed air reservoirs also lose their pressure level due to leakages of the storage system. In order to take these unavoidable losses into account, the key figureenergy lossis necessary. It is defined as the share of the current energy content which gets lost every time period in %s, in the planning horizon.
3.4.6. Suppliers
The linking between flexible loads plays a fundamental role in modeling systems with energy storages. For example, a product warehouse can be filled by different production systems or a compressed air reservoir by different compressors. Depending on thesuppliersor the storage facility, a specific efficiency is achieved with which the energy storage facility is filled. Thus, two machines which fill the same warehouse can produce the same product with different efficiency. If the product is now considered with an energy equivalent, this results in a different conversion efficiency for the two machines. The same applies to two compressors filling a compressed air reservoir with different degrees of efficiency. Not only is the efficiency of the energy converter relevant, but also the storage type. For example, a 12 bar compressed air storage is charged with a significantly lower degree of efficiency than a 6 bar storage. For this reason, the linking between a flexible load and storage is modelled via an ID of thesupplierwith an associated efficiency description. The degree of efficiency can depend on all key figures of thesupplier.
3.4.7. Drain
In many cases, unchangeable loads must be served during production. In contrast tosuppliers, adraindoes not provide any flexibility and therefore only represents a fixed deterministic demand.
In the data model, thedrainis therefore given by a functiond:H!Rwhich assigns to every time in the planning horizon the power in kW which is flowing off.
3.4.8. Costs
Costscan occur not only during the conversion of energy, i.e., with regard to flexible loads, but also at the time of storage. Certain charging strategies can lead to increased storage wear, which in turn increases costs in the long term. For example, lithium ion batteries do not withstand high power gradients or deep discharges. We assume that thecostsof storage only depend on its (time-dependent) energy content. It is important to note that this figure only includes storage-relatedcosts.Costsarising from the flexible operation of thesuppliersmust not be taken into account here since they are already included in the data model for flexible loads.
3.4.9. Summary: Storages
The derived key figures enable the modeling of various storages, e.g., product or electricity storages in industry. Note that the key figures of storage are in general not interrelated with other key figures of flexible loads, dependencies, and storages. However, there are two important exceptions:
First, the conversion efficiency associated with asupplier, i.e., a flexible load, may depend on key figures of precisely this flexible load. Second, thecostsinduced by storage may only depend on the (time-dependent) energy content of the respective storage. The key figures contained in the data model and the associated types, units, and descriptions are summarized in Table3.
Table 3.Key figures for storages.
Key Figure Type Unit Description
Storage id String - An identifier for storage in the company’s
IT system.
Usable capacity 2R kWh
Usually given by an interval whose lower bound of storage energy content may never be undershot and whose upper bound of energy content may never be exceeded.
Initial energy content
incl. time stamp R⇥H (kWh, s) Energy content of the storage at the given time stamp.
Target energy content
incl. time stamp 2R⇥H (kWh, s)
The energy content which the storage has to exhibit at the time stamp (which needs to be contained in the planning horizon).
Energy loss [0, 1] %·s 1
Share of the energy content which gets lost every time period, e.g., due to exchange with
the environment.
Suppliers ⇣
string⇥2R⌘n (kW, - )
A set of flexible loads which supply the storage.
With each supplier, there comes an additional parameter, namely conversion efficiency. Note that the conversion efficiency may depend on the key figures of the associated supplier flexible load.
Drain Abb(H;R) (s7!kW) An unchangeable load which must be served
during production.
Costs Abb(Abb(H;R);R) ((s7!kWh)7!e)
Costsassociated with the usage of the storage, depending only on the (time-dependent) energy content of the storage.
